I'm extremely frustrated and desperate, please help.
Yesterday I was given a 16 GB iPhone 3GS on ATT. I jailbroke it and unlocked it using Ultrasnow and proceeded to download apps and just enjoy it. I've had a TMobile SIM card inside of it, but for whatever reason it was never recognized, just kept saying Searching where it says Carrier.

Anyway, I downloaded Winterboard (or whatever that app for themes is called?) and it prompted me to restart my iPhone. So I did, and from there it got stuck on a white screen. I've tried rebooting it through redsn0w, and it always goes back to a white screen. iTunes recognizes it as in recovery mode, and asks to restore it, however it doesn't let me! I've tried everything, but no matter what it'll say "iPhone software update cannot be contacted" or something like that. Please help, this has been an incredibly frustrated experience.

I've had this issue before. I would replace the battery, which only costs like $20 on iFixit. When you replace the battery, make sure that ALL the connectors are snug - I've gotten the white screen after putting my phone back together when one of the connectors (usually the display connector) are not snug.